nLab
symplectic leaf

Contents

Idea

For (X,{,})(X, \{-,-\}) a Poisson manifold, a symplectic leaf is a maximal submanifold YXY \hookrightarrow X on which the Poisson bracket restricts to a symplectic manifold structure.

XX is foliated by its symplectic leaves.

References

Regular foliations by symplectic leafs have originally been found and studied in

  • F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz & D. Sternheimer, Deformation theory and quantization, Ann. Phys. I l l (1978) 61-151.

A detailed technical review is in the notes

  • Jordan Watts, An introduction to Poisson manifolds (2007) (pdf)

Revised on April 23, 2013 20:50:26 by Urs Schreiber (131.174.42.75)